Self-interacting dark matter provides a promising alternative for the cold dark matter paradigm to solve potential small-scale galaxy formation problems. Nearly all self-interacting dark matter simulations so far have considered only elastic collisions. Here we present simulations of a galactic halo within a generic inelastic model using a novel numerical implementation in the Arepo code to study arbitrary multi-state inelastic dark matter scenarios. For this model we find that inelastic self-interactions can: (i) create larger subhalo density cores compared to elastic models for the same cross section normalisation; (ii) lower the abundance of satellites without the need for a power spectrum cutoff; (iii) reduce the total halo mass by about 10%; (iv) inject the energy equivalent of O(100) million Type II supernovae in galactic haloes through level de-excitation; (v) avoid the gravothermal catastrophe due to removal of particles from halo centers. We conclude that a ~5 times larger elastic cross section is required to achieve the same central density reduction as the inelastic model. This implies that well-established constraints on self-interacting cross sections have to be revised if inelastic collisions are the dominant mode. In this case significantly smaller cross sections can achieve the same core density reduction thereby increasing the parameter space of allowed models considerably.
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